On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions

Abstract

Let Ω be open bounded set of IRⁿ, whose boundary us of cluss C² and let Ω(∞) be thcx set ofwhzch lic at a dtstance less than ∊ of Ω. CVt show that the p-th czqenvalue converges to the p-th eigenvalue λ of the Laplace-Beltrami oprator on δω. Ifλ_p Ap as sztnple, we give limit of . as ∊ tends to 0. These results are written zn thc language of analysis , and no knowledge of differntial geometry assumed.

Keywords:

• laplace operator
• Neumann boundary conditions